Algebraic Set Theory
Algebraic Set Theory

Author: André Joyal

Publisher: Cambridge University Press

Published: 1995-09-14

Total Pages: 136

ISBN-13: 9780521558303

DOWNLOAD EBOOK

This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.

A Book of Set Theory
A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

Published: 2014-07-23

Total Pages: 259

ISBN-13: 0486497089

DOWNLOAD EBOOK

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Set Theory and Logic
Set Theory and Logic

Author: Robert R. Stoll

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 516

ISBN-13: 0486139646

DOWNLOAD EBOOK

Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Labyrinth of Thought
Labyrinth of Thought

Author: Jose Ferreiros

Publisher: Springer Science & Business Media

Published: 2001-11-01

Total Pages: 472

ISBN-13: 9783764357498

DOWNLOAD EBOOK

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Set Theory: The Structure of Arithmetic
Set Theory: The Structure of Arithmetic

Author: Norman T. Hamilton

Publisher: Courier Dover Publications

Published: 2018-05-16

Total Pages: 289

ISBN-13: 0486830470

DOWNLOAD EBOOK

This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

Introduction To Set Theory
Introduction To Set Theory

Author: A. K. Sharma

Publisher: Discovery Publishing House

Published: 2010

Total Pages: 130

ISBN-13: 9788171418770

DOWNLOAD EBOOK

This book Introduction to Set Theory is very important in the field of modern algebra. It is very important to study this book to study modern mathematics. This book contain preliminary Notation, Sets, Subsets, Mapping Function and Relation. This book is useful to the students of under graduate, post graduate students and the candidate appearing in various competitions like pre Engineering/I.A.S/ P.C.S. etc. Contents: Preliminary Notation, Relations, Product or Composite of Mapping, Mapping or Functions

Model Theory and Algebraic Geometry
Model Theory and Algebraic Geometry

Author: Elisabeth Bouscaren

Publisher: Springer

Published: 2009-03-14

Total Pages: 223

ISBN-13: 3540685219

DOWNLOAD EBOOK

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.

Toposes and Local Set Theories
Toposes and Local Set Theories

Author: John L. Bell

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 290

ISBN-13: 0486462862

DOWNLOAD EBOOK

This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Basic Category Theory
Basic Category Theory

Author: Tom Leinster

Publisher: Cambridge University Press

Published: 2014-07-24

Total Pages: 193

ISBN-13: 1107044243

DOWNLOAD EBOOK

A short introduction ideal for students learning category theory for the first time.

An Introduction to Algebraic Structures
An Introduction to Algebraic Structures

Author: Joseph Landin

Publisher: Courier Corporation

Published: 2012-08-29

Total Pages: 275

ISBN-13: 0486150410

DOWNLOAD EBOOK

This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.